Surface Area of Cube and Cuboid
2026-02-28 19:11 Diff
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Last updated on August 5, 2025

A cube and a cuboid are 3-dimensional shapes with flat surfaces. The surface area of these shapes is the total area covered by their outer surfaces. In this article, we will learn about the surface area of a cube and a cuboid.

What is the Surface Area of a Cube and a Cuboid?

The surface area of a cube and a cuboid is the total area occupied by their boundaries or surfaces. It is measured in square units.

A cube is a 3D shape with six equal square faces, while a cuboid has six rectangular faces. Both shapes have a total surface area, which is the sum of the areas of all their faces.

Surface Area of a Cube and a Cuboid Formula

Both a cube and a cuboid have six faces, and their surface areas are calculated by summing the areas of all these faces. Below are the formulas for calculating their surface areas.

For a cube: Total Surface Area (TSA) = 6a² Here, a is the length of a side of the cube.

For a cuboid: Total Surface Area (TSA) = 2(lb + bh + hl) Where l is the length, b is the breadth, and h is the height of the cuboid.

Surface Area of a Cube

The surface area of a cube is the total area of all six identical square faces. The formula to calculate the surface area of a cube is:

Surface Area = 6a² square units

Here, a is the side length of the cube.

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Surface Area of a Cuboid

The surface area of a cuboid is the sum of the areas of all its rectangular faces. The formula to calculate the surface area of a cuboid is:

Surface Area = 2(lb + bh + hl) square units

Where l is the length, b is the breadth, and h is the height of the cuboid.

Volume of a Cube and a Cuboid

The volume of a cube is the space it occupies, calculated as: Volume of a cube = a³ cubic units

The volume of a cuboid is the space it occupies, calculated as: Volume of a cuboid = l × b × h cubic units

Confusing Side Length with Edge Length

Students sometimes confuse the side length of a cube with the edge length of a cuboid. Remember, in a cube, all edges are equal, while a cuboid has different edge lengths.

Problem 1

Given a = 4 cm. Use the formula: Surface Area = 6a² = 6 × 4² = 6 × 16 = 96 cm²

Okay, lets begin

Find the total surface area of a cuboid with length 5 cm, breadth 3 cm, and height 2 cm.

Well explained 👍

Problem 2

Use the formula: TSA = 2(lb + bh + hl) = 2(5 × 3 + 3 × 2 + 2 × 5) = 2(15 + 6 + 10) = 2 × 31 = 62 cm²

Okay, lets begin

A cube has a side of 7 cm. Find the total surface area.

Explanation

Surface Area = 294 cm²

Well explained 👍

Problem 3

Use the formula: Surface Area = 6a² = 6 × 7² = 6 × 49 = 294 cm²

Okay, lets begin

Find the surface area of a cuboid with dimensions 6 cm by 4 cm by 3 cm.

Explanation

TSA = 108 cm²

Well explained 👍

Problem 4

TSA = 2(lb + bh + hl) = 2(6 × 4 + 4 × 3 + 3 × 6) = 2(24 + 12 + 18) = 2 × 54 = 108 cm²

Okay, lets begin

The surface area of a cube is 150 cm². Find the side length.

Explanation

Side length = 5 cm

Well explained 👍

It is the total area of all six square faces of the cube, calculated as 6a².

1.What is the surface area of a cuboid?

It is the sum of the areas of all six rectangular faces of the cuboid, calculated as 2(lb + bh + hl).

2.How is the volume of a cube different from a cuboid?

The volume of a cube is a³, while the volume of a cuboid is l × b × h.

3.What units are used for surface area?

Surface area is always measured in square units like cm², m², or in².

4.Can a cube be considered a cuboid?

Yes, a cube is a special type of cuboid where all edges are equal.

Common Mistakes and How to Avoid Them in the Surface Area of Cube and Cuboid

Students often make mistakes while calculating the surface area of a cube and a cuboid, leading to incorrect answers. Below are some common mistakes and ways to avoid them.

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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

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: She has songs for each table which helps her to remember the tables